Problem: Simplify the following expression: $ n = \dfrac{-7}{2} + \dfrac{-4p - 9}{p - 3} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{p - 3}{p - 3}$ $ \dfrac{-7}{2} \times \dfrac{p - 3}{p - 3} = \dfrac{-7p + 21}{2p - 6} $ Multiply the second expression by $\dfrac{2}{2}$ $ \dfrac{-4p - 9}{p - 3} \times \dfrac{2}{2} = \dfrac{-8p - 18}{2p - 6} $ Therefore $ n = \dfrac{-7p + 21}{2p - 6} + \dfrac{-8p - 18}{2p - 6} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-7p + 21 - 8p - 18}{2p - 6} $ $n = \dfrac{-15p + 3}{2p - 6}$